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<b>let </b><font color="Maroon">q1</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">q2</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">p1</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/><b>let </b><font color="Maroon">p2</font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>







<b>assume </b><a NAME="E1:21"/>
<span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">q1</font>,<font color="Maroon">q2</font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> <a href="xboole_0.html#NR5" target="_self">meets</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">p1</font>,<font color="Maroon">p2</font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span>
 ;<br/>

<b>then consider </b><font color="Maroon">x</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:21"/><i><font color="Green">E22</font></i>: 
( <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">q1</font>,<font color="Maroon">q2</font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> &amp; <font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="rcomp_2.html#K1" target="_self">[.</a><span class="default"><font color="Maroon">p1</font>,<font color="Maroon">p2</font></span><a href="rcomp_2.html#K1" target="_self">.[</a></span> )
 <b>by </b><i><a class="ref" href="xboole_0.html#T3">XBOOLE_0:3</a></i>;<br/>
<b>reconsider </b><font color="Maroon">x2</font> = <font color="Maroon">x</font> as   <a href="real_1.html#NM1">Real</a> <b>by </b><i/>;<br/>
<a NAME="E5:21"/><i><font color="Green">E23</font></i>: 
( <font color="Maroon">q1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">x2</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">q2</font> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E6:21"/>
( <font color="Maroon">p1</font> <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">x2</font> &amp; <font color="Maroon">x2</font> <a href="xxreal_0.html#NR3" target="_self">&lt;</a> <font color="Maroon">p2</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E7:21"/>
<font color="Maroon">q2</font> <a href="xxreal_0.html#NR2" target="_self">&gt;=</a> <font color="Maroon">p1</font>
 <b>by </b><i>, <a class="ref" href="xxreal_0.html#T2">XXREAL_0:2</a></i>;<br/>


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